L.. Policy Research 4 JN)4r 3 9t 43
WORKING PAPERS
Debt and International Finance
International Economics Department
The World Bank
August 1992
WPS 943
Burden-sharing
among Official
and Private Creditors
Asih Demirgui-Kunt
and
Eduardo Fernandez-Arias
Official creditors - especially multilaterals - have absorbed
more of the burden of the debt crisis than private creditors have.
Official creditors are not necessarily weaker or less senior, but
for the sake of nonfinancial objectives, they may be unwilling
(rather than unable) to exercise their substantial enforcement
power.
ThePolicy ResearutWoking Papa: dissminstethefindings of work inprogressa ndencouragetheexchangcof ideas among Bank staff
and all others intmrestd in dcelopment issues. Iles papers, distnbuted by the Research Advisory Staff, carry the names of the authors,
reflectye attrvieva and shod beusod and eited ordgly. lct dings.intzpmn atioms, andconclusioo s aem theauthors'own.y
should not be attnwbuted to fth Wodd Bank, its Board iof Direaors, its managernenl, or any of its mrnber comuitns.
t ~~~~~~~~~~~~~~~~~Policy Research
Debt and International Finance
WPS 943
This paper - a product of the Debt and International Finance Division, International Economics Department - is
part of a larger effort in the department to understand the economic relationships between developing countries and
external creditors regarding credit rationing and debt negotiations. Copies of the paper are available free from the
World Bank, 1818 H Street NW, Washington DC 20433. Please contact Karin Waelti, room N9-043, extension 37664
(August 1992, 31 pages).
Demirgtli-Kunt and Femandez-Arias analyze how the To assess burden-sharing, the unobservable
burden of the debt crisis has been sf.ared by various implied prices of official debt need to be cstimated.
classes of creditors. Given the rising share of official The authors first analyze how, in a seniority-based
debt in the total debt of developing countries, official corporate debt model, information on these implied
creditors have a growing need to develop a burden- prices can be recovered by looking at the differential
sharing indicator. impact of various stocks of debt on the market price.
They analyze the validity and drawbacks of this
This paper represents the very first step in this model for the sovereign debt case and conclude that
direction. So, its analysis narrowly focuses only on seniority sharing rules are probably not appropriate.
financial profits. No inference should be made They then show that implied prices are still identified
regarding the overall performance of official credi- under more general sharing rules, which allows us to
tors, whose evaluation requires the assessment of relax that assumption and still be able to derive
their nonfinancial objectives. Similarly, no inference relevant inferences. A suitable multicreditor debt
should be drawn regarding the solvency of valuation model, dependent on the stock of private
multilaterals, which is essentially determined by debt and !he debt shares of various creditors, is then
external guarantees. Extensive further research is derived and estimated.
required to shed light on these areas and to eventually
derive the relevant policy conclusions. The empirical estimations show weak effects of
the official debt stocks on the market price and
The authors briefly review the relative perfor- suggest that the' implied prices of official creditors are
mance of external creditors during the debt crisis in lower than the market price, especially for multilat-
terms of exposure, net transfers, and arrears. They eral creditors. This finding implies that official
argue, however, that a meaningful measure of burden- creditors have, relative to private creditors, absorbed a
sharing needs to go beyond those observations and larger burden, especially multilaterals. But it does not
consider the capital losses that creditors have made on imply that official creditors are weaker or less senior:
outstanding debt stocks. So, they develop a finan- official creditors may be unwilling, rather than
cially sound measure of rate of return - incorporat- unable, to exercise their substantial enforcement
ing repayment flows and capital losses - and derive power for the sake of nonfinancial objectives. Two
a financially sound definition of burden-sharing. This qualifications to the findings on implied prices: First,
definition is then applied to a group of severely the "single collateral" assumption of corporate debt
indebted countries for which secondary market prices may not be applicable to sovereign debt. The evi-
are available. The finding: private creditors made a dence may also be consistent with undiscounted
loss of about 30 percent during the debt crisis, and official implied prices if official creditors have
official creditors avoided absorbing a comparable independent enforcement mechanisms not available to
burden only if, on average, the implied prices of their private creditors. Second, the class of admissible
debt stocks were significantly higher than market si,aring rules used for identification generalizes the
prices. seniority rules but may still exclude the relevant
sharing rule.
The Policy Research Working Paper Series disseminates the findings of work under way in the Bank. Anobjective of the series
is to get these findings out quickly, even if presentations are less than fully polished. The findings, interpretations, and
I conclusions in these papers do not necessarily represent official Bank policy.
Produced by the Policy Research Dissemination Center
Table of Contents
I. Introduction 2
II. Relative Performance of External Creditors during the Debt Crisis 4
III. Background and Definitions 5
IV. Equal Burden Sharing Implications 8
V. A Multi-Creditor Debt Valuation Model 9
Generality and limitations of the model 13
VI. Empirical Evidence 15
VII. Conclusions 17
Refeiences 19
Tables 20
Appendix 26
2
I. INTRODUCTIL.N
This paper seeks to determine how the burden of the debt crisis is being shared among different
creditors, particularly private creditors, multilateral creditors, and bilateral creditors. Burden sharing
among creditors is not a well defined concept. One popular measure of how the burden is being shared
is given by the observed trends in the changing composition of the external debt portfolio of debtor
countries, which is a reflection of the financial flows connected to debt service and new lending as well
as debt conversions. Significant as these trends may be for the evolution of the debt crisis, burden
sharing cannot be measured by simply looking at net transfers received or new money provided by each
creditor class. Determining burden sharing among creditors requires determining capital losses and gains
in their stock of debt.
This paper addresses the issue of how capital losses and gains are shared by creditors. However,
this issue is still narrow since, while private creditors only care about their financial position, official
creditors have other concerns as well, such as the development impact in the case of development
institutions such as IBRD. Nevertheless, a purely financial analysis is useful because financial losses in
a given country reduce lending capacity elsewhere and therefore result in an additional constraint on the
optimal allocation of funds for development or other relevant purposes. It should be emphasized at the
outset that precisely because international financial institutions have non-financial goals to which financial
returns are subsidiary, their performance should not be evaluated narrowly from a financial viewpoint.
To the extent that the best policy suited for their purpose is followed, which may imply financial losses,
they would remain useful institutions and, therefore, the support of their shareholders can be expected.
The credit rating of these institutions is determined by this backing, both through explicit and implicit
guarantees. Therefore credit ratings of IFIs depend on good performance with respect to their specific
objectives and not on financial performance alone. In the case of official creditors, financial returns are
one component of the analysis rather than the bottom line. This paper only focuses on this component.
Capital losses arise because the financial value of debt claims, as measured by the present value
of the resources that the debtor can be expected to make available for their service, can fall below its face
value'. While the secondary market price of debt reflects the capital losses on debt held by commercial
banks, the absence of a market makes the corresponding price of official debt claims unobservable. How
the implicit price of official debt and the price of private debt relate is controversial: while some opine
that official creditors are implicitly more senior, others think that they have a weaker bargaining position
and are consequently less senior.
The literature on burden sharing is very scanty. Dooley (1990) was the first author to emphasize
that a financially sound measure of burden sharing among creditors needs to look at the capital losses
made on outstanding debt. He constructs a measure of burden in terms of the rates of return on total
claims. However, a fundamental limitation of the Dooley analysis is that it is basically an accounting
framework. Simulation results depend entirely on the assumed relative seniority between official and
private creditors. The issue of seniority of official creditors, and of multilaterals in particular, is not
addressed, which makes the simulations less useful.
'This disregards other factors affecting the financial value of debt, such as the implicit deposit insurance subsidy
that commercial banks receive by holding impaired debt claims. Note that in this case the financial value of debt
would overestimate the country's expected payments.
3
Although there are many who believe that official creditors are more senior than private creditors,
Sjaastad (1990) and more recently Bulow and Rogoff (1991) have questioned the World Bank's senior
creditor status.2 Finally, Berthelemy and Vourc'h (1991) empirically estimate burden sharing among
creditors. However, their estimated value of official claims is based on the assumption that official
creditor claims are impaired. Thus they estimate the ability of capturing net transfers in the future based
on the analysis of the net transfers creditors have been able to extract in the past, and show that the
burden is being shared in inverse relation to the proportion of net transfers received from debtor
countries. However, there is no real basis for this assumption.
This paper addresses both the relative seniority and burden sharing of different creditor classes.
The implied prices for equal burden sharing during the debt crisis are derived. A ranking of implied
prices for different creditor groups is estimated within a multi-creditor valuation model of private debt
that does not assume the existence of a seniority structure. Burden sharing among creditors is determined
based on these implied prices. Our valuation is forward looking, i.e., it is based on future expected net
transfers rather than past net transfers.
The paper consists of seven sections. The next section discusses the relative performance of
external creditors during the debt crisis, analyzing historical trends. Section III defines -iIe concept and
measure of burden sharing and Section IV derives implications of equal burden sharing during the debt
crisis. Section V constructs an analytical multi-creditor debt valuation model, which is empirically
estimated in Section VI. Finally, section VII concludes the analysis.
2After the first draft of this paper was written, two more pieces make the case of equal seniority between private
and official creditors following similar methods: Bulow, Rogoff, and Bevilaqua (1992) and Cohen (1992). This
paper discusses the restrictive assumptions that are needed to justify those methods, which are implicit in both
papers.
4
II. RELATIV7E PERFORMANCE OF EXTERNAL CREDITORS DURING THE DEBT CRISIS
Performance of different creditors during the debt crisis has been sharply differentiated. In what
follows, a comparative analysis long-term debt of multilateral, bilateral, and private creditors is presented.
This presentation discriminates between Severely Indebted Middle Income Countries (SIMICs) and non-
SIMICs (the rest of the developing countries except those not credit constrained), following the definitions
in World Debt Tables unless otherwise indicated.
The level of developing country external debt has increased and its composition changed
substantially over the course of the debt crisis. It is clear that since the beginning of the debt crisis in
1982, multilateral creditors are the ones increasing their exposure the fastest, private creditors are
retrenching and bilateral creditors are in between. This has led to substantial changes in the composition
of external debt portfolios as shown Table 1: the share of multilateral creditors persistently increases at
the expense of the share of private creditors. Bilateral creditors also increased their share overall,
although it slightly decreased in non-SIMICs. These changes are more marked in the SIMICs, where the
proportion of multilateral and bilateral credit in private credit grew,in the period 1982-1989, from less
than 10% and 20% to more than 20% and 40% respectively.
A substantial part of the growth in debt stocks expressed in dollars is due to the fact that on
average the dollar depreciated in relation to other currencies in which extemal debt is denominated. If
debt stocks are corrected by valuation changes3, lower stocks are obtained. In particular, private creditors
in SIMICs would have had a reduction in exposure. As shown in Table 1, in this case the share of
multilateral creditors would have been even higher in both SIMICs and non-SIMICs. In particular, the
proportion of multilateral debt in private debt is even higher considering these adjusted debt stocks (the
opposite is true for bilateral creditors). The fact that in share terms private creditors decreased their
exposure measured in dollars at the expense of official creditors, particularly multilateral creditors, cannot
be attributed to lower exchange rate capital gains but to their performance in relation to the amount of
net transfers they have extracted from debtor countries.
Figure 1 shows net amounts transferred in relation to outstanding debt, which is the key factor
explaining the evolution of adjusted debt stocks. While private creditors have been extracting net
resources since the beginning of the crisis at sizable rates, by and large official creditors, and in particular
multilateral creditors. have been providing net resources which have partially compensated the private
creditors extraction.
Another interesting dimension of the process relates to arrears. Arrears have been accumulating
at a rapid rate, as shown in Figure 2. It is very clear, however, that they have been falling mostly on
bilateral and private creditors, while multilateral creditors have managed to avoid arrears to a large
extent4. Arrears are for the most part a problem of SIMICs. In this group of countries, as of the end of
19b0, accumulated arrears represent around 20% of bilateral and private debt and around 5% of
3Valuation changes were estimated as the difference between the change in the stock of debt augmented by debt
reduction on the one hand, and net flows and interest rescheduled on the other. Therefore what is reported under
valuation changes includes errors and omissions.
41t should be noted that the previous definition of arrears includes not only accumulated interest arrears, as
reported in WDT, but also their capitalization (at rates similar to the ones on current service due).
5
multilateral debt. The record about reschedulings is similar to the one discussed for arrears: multilateral
creditors have not rescheduled debt, while private and bilateral creditors have done it repeatedly.
This picture is consistent with multilateral creditors providing positive net transfers in retribution
to full debt service and private creditors extracting net transfers through receiving partial payment of debt
service due, which is renegotiated in the form of a rescheduling agreement or arrears. The case of
bilateral creditors falls somewhere in between.
III. BACKGROUND AND DEFINITIONS
In this section we start the analysis of the evidence by looking at claims held by private creditors
and measuring their losses. We then generalize the concepts to official creditors and define burden-sharing
among all of them.
Let D[tl be the face value of private debt claims at the end of period t and V[t] its financial value.
Let p[tI=V[t]/D[t] be the implied price of face value debt. If a secondary market for debt exists, p[t]
would be the market price5 and V[t] would be the market value of debt, that is the opportunity cost of
holding the claims. Let T[t] be the net transfer received from the debtor at the end of period t. Then the
realized rate of (economic) profit x is such that:
(1) 1 +x = (V[t]+T[t])/((1 +i)V[t-1]))
(p[t]D[t] +T[tl)/(( + i)p[t-l]D[t-11))
where i is the market discount rate in period t (the opportunity cost of holding a unit value during period
t). In market equilibrium, the expected rate of profit x is zero.
In order to analyze how losses may come about, consider first the simplest case where debt
service obligations are always honored. In this case the financial value of claims, that is their mE iket
value, is the expected present discounted value of contractual debt service. Assuming that there is
competition among creditors, this value coincides with the face value of debt. In other words, the
competitive market rate i is charged and expected p[t]=1 for all t. Then expected x=O because
(D[t]+T[t])/((1+i)D[t-1]))=1. In this case with no sovereign risk, these equalities also hold ex-post if
it is assumed that future market discount rates are certain, which we assume in what follows in order to
focus on sovereign risk. It is easy to check that in this case the expected profit rate x is unaffected by
the transfer T[t] made under the particular debt service schedule of the contract, because the associated
compensatory changes in face value debt D[t] would be valued at par. In particular, new lending at time
t would lead to zero profit. Therefore, lending would be voluntary and there should not be any difficulty
in rescheduling debt service.
Suppose, by contrast, that with some positive probability contractual debt service may not be met.
If this possibility arises for liquidity reasons but solvency is not an issue (in the sense that debt obligations
would be expected to be met in the future if rescheduled), then the no sovereign risk case would still
apply and previously contracted obligations would be met by additional borrowing at risk-free rates.
However, if solvency is uncertain sovereign risk becomes relevant. In this case, if solvency conditions
5Like in stock prices, there is a possibility of price bubbles not reflecting fundamentals which will be disregarded
for simplicity. It should be noted however that in no case can prices be below fundamentals (i.e the country's
expected present value service), because in that case it would be more profitable to hold to the asset and there would
be no seller. In other words, bubbles can only be explosive, as opposed to implosive. This implies that bubbles
cannot be an explanation for low secondary market prices of debt.
6
deteriorate to the point that the market value of debt V[ti falls below face value debt D[t], ex-post p[t]
would consequently fall below unity. To the extent that p[t-1] = 1, lending at time t-1 is voluntary and
therefore, as before, x is expected to be zero by virtue of lenders' competition. In this case, however,
a risk premium r needs to be charged in order to compensate for the possibility that x be negative ex-post.
The feasibility of this risk-offsetting premium, in turn, would justify the voluntary nature of the lending
under these circumstances.
Suppose for simplification that loans are made for one period in the amount D[t-11 and that, as
perceived at t-1, an adverse shock imposing a ceiling S on present value debt service from period t
onwards will occur with probability s. Then the contractual debt service at period t is (1 +i)(1 +r)D[t-1].
If the shock does not occur, the rate of profit r is realized. If it occurs. a negative rate of profit
h=S/(1+i)D[t-1]-1 is realized (under the assumption that S
7
For example, lending by official creditors may not be profit-maximizing. This may occur by design,
because official creditors may look at dimensions beyond narrowly defined financial results. It may also
occur because of the lack of market controls on poor performance, such as stock quotations or buyouts.
This may reflect in appropriate risk-premi.. not being charged when non-negative profits are feasible. It
may also reflect in willingness to lend when the optimal strategy, from a purely financial point of view,
would be to attempt to withdraw as private creditors do. A strategy which is suboptimal from a narrow
financial point of view may be globally optimal for a creditor government or a development institution.
The case can be made that performance of official creditors should be measured in a more comprehensive
way. An attempt to do so may hide poor performance, however. Here we prefer to stick to our financial
measure of burden and rate of profit k3eping in mind its limitations. This purely financial measure has
the additional advantage of leading to an unambiguous definition of burden-sharing, which would be
subjective if idiosyncratic factors were introduced.
With these considerations in mind, formula (1) can be also applied to official creditors. Its content
is mostly conceptual, however, because the imputed price of debt p[.1 and its value V[.! ire not observed.
More generally, let j index creditor classes. Let Dj[t] be the face value of creditor j debt claims at the end
of period t ai.u -V--j-.j uie expected present discounted v;lue of its associated debt service (given the lending
strategy followed by creditor j). Let pj[t1 =Vj[t]/D,[tj be the implied price of face value debt. Let Tj[t]
be the net transfer received from the debtor at the end of period t. Then the realized rate of (economic)
profit in period t, xj[t-l,t] is such that:
(2) 1+xj[t-l,t] = (Vj[t]+Tj[t])/((l+i)Vj[t-1]))
= (pj[t]Dj[t] +Tj[t])/(( + i)pj[t- l]Dj [t-1]))
where i is the market discount rate in period t.
The rates xj can be interpreted as the gain per unit of original value. In the context of losses they
would be negative. Let x be the average profit rate computed lumping together all creditors. It is easy
to check that it is a weighted average of the profit rates xj weighted by weights wj, where wj is the share
of V,[t-1] in total value at the beginning of period t. In the case that profit rates xj are the same for all
creditors, and therefore equal to x, we say that profits are equally shared. Assuming that x < 0, this is
the case of equal burden sharing. More generally, we say that the lower (the more negative) X,, the larger
the creditor j's share of the burden.
Expression (2) and the definition of burden-sharing can be extended to cover a longer period
where a stream of transfers is made or received. Consider the case where transfers are received over t-to
years. Let Tj[to,t1 be the present value of the stream of net transfers to creditor j in the period (to,t)
discounted forward to period t.
8
Tlhen
(3) 1+xj[to,tJ = (Vj[t]+Tj[to,t])/((l+I)Vj[3t0)
Tj[tO,t1/((l +I)pj[tO]Dj[tOj) + pj[t]Dj[tI/((1 +I)pj[to]Dj[to])
where I is the discount rate for the entire period (tj,t).
Expression (2) is a particular case of expression (3) when to =t-1. Expression (2) can be seen as
a definition of marginal burden and leading to a definition of marginal burden-sharing in relation to
period t. Expression (3) can be interpreted as a similar concept but related to total burdens and
burdensharing over the entire period. Both concepts relate to gains or losses in reiation to the value of
claims in the base year. Therefore the marginal concept focuses on how the new iiurden is shared,
irrespective of how the past burden was shared. The total concept, in contrast, if appliec to a past period,
summarizes how the total burden generated in the period was shared. It is easy to chec'- that xj[tk,t1 =
xj[to,t-1] + a[tO,t-l1.xj[t-l,t], where a>O is the ratio of the mark3t value of debt at t-I and at to. As
discussed above, the marginal profit rate xjft-l,t] has zero expected value at time (t-1). Since then a[tO,t-1]
is fixed, total profit rate is a martingale and fo!lows a random walk. This implies that losses are
accumulated over a period only through unexpected adverse realizations.
IV. EQUAL BURDEN SHARING IMPLICATIONS
In what follows we will use three creditor classes: private, official multilateral, and official
bilateral. The subindex j will be correspondingly substituted by p,m and b. When a distinction is made
only between private and official creditors, the letters p and o are used.
The debt crisis can be characterized within the above framework. In the lending phase, say
between 1973 and 1982, risk premia were charged by private lenders to cover the risk of adverse shocks
putting a binding constraint on the value of debt outstanding. In this period the implicit price of private
debt was unity, lending was voluntary and expected profits were zero. Until 1982 such a shock did not
occur, which led to positive ex-post profits. In 1982 a sufficiently big adverse shock in terms of terms
of trade and interest rates occurred, which led to ex-post negative profits in a great number cf/countries.
This situation remains very much unchanged until now, since in those countries private lending remains
involuntary and secondary market prices quote at a substantial discount. It should be remembered that
the ex-ante zero profit condition applies in every period, whether lending is voluntary or not. Therefore
ex-post capital gains or losses during the entire period have been realized to the extent that unexpected
events occurred.
The ex-post gains of private creditors before 1982 may have compensated the ex-post losses after
that date. Even if this is not so, since ex-ante profits are zero and lending was voluntary before 1982,
ex-post losses should not be seen as meriting any particular compensation. In an ex-ante sense there is
no burden. In an ex-post sense there is a burden which depends on when we want to start accumulating.
The burden would be smaller, perhaps negative, if ex-post profits are accumulated since the beginning
of the lending boom in 1973. We leave that exercise for further research and concentrate on the ex-post
return obtained after the breakdown in 1982 until 1989. This is done by using formula (3) to obtain:
(4) 1 +x= T/(1 +I)V[19821 + V[1989]/(1 +I)V[19821
T/(1 +I)D[19821 + p[1989]D[19891/(1 +I)D[19821
where I is the discount rate for the entire period 1982-1989 (the compounded Libor rate in the period)
and T is the present value of the net transfers received during the period discounted forward to 1989. The
initial stock of debt is valued at par.
9
Applying (4) to private creditors, the first term can be interpreted as the fraction of initial
investmient that private creditors have been able to recover by extracting net transfers in the period. It
amounts to almost 50% for the SIMICs (0.4941). The return is higher than this, however, because the
capital loss has not been complete and the remaining debt has a positive value, which equals the expected
additional fraction that can be recovered in the future. Tle above caiculation requires an estimate of
p[19891. For SIMICs this can be calculated as a weighted average of secondary market prices in those
countries quoted at the end of 1989, where the weights reflect the importance of each country in -1 ivate
creditors SIMIC portfolior . We obtain pg 19891=0.294, which leads to a residual value of almost 20%
(0. 1947). Then 1+ x = 0.4941 +- 0.1947 = 0.6888. This implies that the rate of profit x =-31.12%
We now pose the question of how the other creditors are doing and how the burden is shared.
To answer that question is not easy. It should be noted at the outset that burden-sharing among
creditors cannot be addressed by simply looking at the trends described in section rs. While net transfers
is relevant for the determination of the burden absorbed by a particular creditor, it is necessary to know
the remaining value of outstanding claims in order to assess it. Since there is no market for multilateral
and bilateral debt, there is no direct market information about it The evolution of exposure, both in
levels and shares, as well as the record of arrears and reschedulings, may provide indications to that
effect but are hardly conclusive. Before turning to the discussion of this issue, we apply (4) and compute
the implicit price of multilateral and bilateral debt which would lead to equal burden-sharing among them
and private creditors for SIMICs. Equal burden-sharing is defined as one in which losses in a given
period are proportional to the original value invested, that is to say, one in which the ex-post rates of
profit are equal.
Since multilateral and bilateral creditors have been transferring resources in net terms to the
SIMICs during the period, the return derived from net transfers extraction is actually negative: -0.3017
for multilateral creditors (of which, -0.2811 for IBRD), and -0.143 for bilateral creditors. For equal
burden-sharing the implicit prices as of end-1989 would be 0.63 14 for multilateral creditors (0.529 for
IBRD), and 0.4653 for bilateral creditors (assuming that the implicit price in 1982 is also unity). This
result indicates that for equal burden sharing between IBRD and private creditors, IBRD claims must be
worth much more than those of private claims (23.5 cents more on the dollar). Only if IBRD claims are
worth more than 52.9 cents on the dollar, private creditors would be sharing more of the burden
associated with the debt crisis. Similar qualitative results apply to other official creditors. This of course
includes the case where IBRD and other official claims are not impaired in any way, in which case
official creditors would not be suffering any burden at all according to this definition.
V. A MULTI-CREDITOR DEBT VALUATION MODEL
After giving this background information about the range of numbers that equal burden-sharing
implies, we return to the conceptual problem of determining the financial value of official creditor claimts.
One first problem is that part of the burden absorbed by official creditors is the grant element of their
concessional loans, which are uxi'i -fitable by design. This would not apply to IBRD, however. More
generally, since they are not proti-maximizers, they cannot be assumed to follow the strategy that a
private creditor would follow. We are conscious that to the extent that part of the financial losses are
purposely not avoided if other concerns are more important (such as large development returns), the very
notion of financial burden may not be entirely appropriate for many purposes. Nevertheless, here we will
81t is assumed that prices of commercial banks apply to all private creditors.
10
only consider the narrow issue of the financial value of claims and stick to the ur1nbiguous financial
definition of burden-sharing.
One way to analyze the problem of the value of official debt is to decompose it into two elements:
the value that would be obtained if the entire debt were sold to a new private creditor, which following
Sjaastad (1990) we call its intrinsic value, and the rest, which can be attributed to the differential creditor
status of official creditors vis-a-vis private creditors. The intrinsic value of official portfolios does not
seem to be worse than private portfolios in SIMICs. Reweighing the secondary market index price for
SIMICs as of end-1989 by the portfolio weights of official creditors, we obtain that the index is 0.33 snd.
0.29 for multilateral and bilateral debt respectively, which has to be compared to the private creditor
index 0.29. The situation for other countries may be different, but the absence of widespread secondary
markets for their debts prevents the application of similar methods.
Regarding differential creditor status the ei idence is less conclusive. While the evidence of low
incidence of arrears and reschedulings in multilateral debt may confirm that multilaterals are preferred
creditors, there are two counterarguments which seriously weaken this conclusion. First of all, it can be
argued that the proposition has not been really tested because the multilaterals are willing to lend
voluntarily, and actually frequently provide positive net transfers. Whilc, receiving, or expec.ing to
receive, positive net transfers, debtor countries would fully service the debt to any creditor, even a non-
preferred one. The very willingness of official creditors to lend may indicate that they do rot think that
their claims are impaired. This argument disregards the distinct possibility that official creditors, not
being profit-maximizers like financial institutions, may be willing to lend at some financial loss if other
dimensions of their utility function are satisfied. In any event, what official creditors "think" is a much
weaker test than the market test to which private creditors are subject to. Second, a more cynical view
of the same facts is that official creditors are forced to provide positive net transfers in exchange for a
formal compliance with scheduled debt service.
The easiest model to consider is one where there is a fixed given pool of resourceQ to be shared
among creditors. If in present value terms this pool amounts to less than the face value of total claims,
there is a conflict among creditors over how to share the loss. This model is consistent with an ability
to pay model, where the pool represents the availability of resources to service debt. To the extent that
there is uncertainty over the availability of resources, it may occur that in some circumstances the
resources exceed total debt claims. Since this excess will not be used to service debt, the relevant
probability distribution of available resources is truncated when all debt claims are fully serviced. The
relevant measure of ability to pay becomes the expected present value of this distribution, which is
therefore a function of total face value. The model is generalized to the case of uncertainty by
considering a given pool of resources equal to this expected present value. To the extent that the pool is
smaller than the face value of debt, there are financial losses to all the creditors combined and conflict
among them as to how to share the loss.
The scanty literature on multi-creditor valuation models has relied on ability-to-pay models and
has modelled the conflict among creditors in terms of a seniority structure. In a seniority arrangement,
there is a pre-established order in which each creditor class can claim and receive payment. This
framework of ability-to-pay and seniority structure is taken from the corporate debt literature, where there
is essentially one unspecific collateral (the value of the firm) to be shared by creditors in the order
specified by the law. We will argue that this framework may not be entirely appropriate to the sovereign
debt case and needs to be generalized. We start building our model by applying this corporate debt
11
framework to sovereign debt, where for simplicity creditors are classified in only two classes: private and
official. There are three cases considered in the literature: official creditors are senior to private creditors,
official creditors are junior to private creditors, and both classes of creditors have the same seniority and
share the loss equally (can claim in proportion to exposure). We now explain the implications of such a
model and later turn to the restrictive nature of its assumptions.
If the corporate seniority model is applied to sovereign debt, the total value of debt of private and
official creditors, V=Vp + V., depends only on total face value D=DP+D0 (the time index is dropped for
clarity), as can be easily checked by looking at the problem from the debtor's point of view, where the
order in which creditors claim is irrelevant. The value V increases with face value D, because there is
some probability that the entire debt can be serviced as explained before (this assumes that the possibly
adverse effect of debt on the country's ability to pay as a result of the so-called "debt overhang" is not
severe enough as to give rise to a debt Laffer curve). This probability can be expected to decrease with
face value of debt. Under these conditions, the value V is an increasing concave function of face value
D (starting at a 45-degree line for low values of D). In Figure 3 this value function V[.] is depicted under
the assumption that official creditors are senior. In this case, the first portion of D is D. with a
corresponding value V0=V[DJ which can be read directly from the graph, as if no other creditor had
any claim. The second and last portion of total face value corresponds to private debt DP. Its value is the
residual value after the senior official creditors are satisfied: VP=V[D0+D]-V[D,i=V-V0.
The imputed price of debt can be represented by the slope of lines OA, in the case of official
creditors, and AB in the case of private creditors. We note that due to concavity, the price of senior debt
is larger than the price of junior debt, and may be one at low levels of debt where the value function is
a 45-degree line. Note that if the face value of a particular class of debt increases by one unit, the price
of that class of debt always falls, be it senior or junior (it can of course remain at one at low levels of
senior debt). The effect on the price of the other class depends on seniority, however. If the class
increasing debt is senior, the price of junior debt will decline even more than with an own-class debt
increase, as can be seen by comparing the slope of A'B' and AB'. If the class increasing debt is junior,
however, no effect would be felt on the price of senior debt. If private debt is senior to official debt, the
graph and conclusion would be obviously reversed. Finally, if both classes share the burden equally, the
price of their debts would be the same and would be equally affected by changes in either class of debt.
This case amounts to assuming that there is only one class of debt with face value D.
The above model and results can be generali :ed as follows. In the spirit of an ability-to-pay
model, we keep the assumption that there is a given pool of resources to be shared. This only assumption
implies that total value V=V0+Vp depends on total face value D=D.+Dp, as opposed to both face values
separately. However, we dispense with the seniority structure assumption and allow more general sharing
rules. In the context of sovereign debt, by contrast to the corporate debt case, this generalization appears
relevant because there is no applicable law determining seniority. Since by definition Vj=pjDj, in an
ability-to-pay model it holds true that
(5) ppDp+p4D0=V[D0+DJ,
where the prices pj are functions of both face values D. and Dp.
Partially differentiating (5) with respect to DP and D., and noticing that both derivatives of V[.J
are equal, we obtain:
(6) pp-po = Dp(dpp/dD. - dpp/dDp) - D0(dp,/dD. - dp0/dD0)
12
Notice that the comparison of own-derivatives and cross-derivatives contain information on the
implied price for official debt, relative to private debt, irrespective of the sharing rules. The intuition
behind these relations is similar to the analysis of the three seniority cases conducted above. The
implications, however, are not restricted to these three cases. Suppose more generally that the sharing
arrangements between creditors are such that the resulting prices move together according to a function
p0=s0[pp].9 The three seniority cases can be accommodated under this assumption: p0=O, p0=pp, and
p0=1. Other functions would reflect different sharing rules, not necessarily reflecting a seniority
structure. In particular, it may correspond to an implicit agreement as to how the burden is going to be
shared. The fact that identity (5) always holds severely restricts the set of admissible functional
relationships between prices if those functions need to apply over the entire range of feasible prices, to
the point that it is not clear whether any meaningful generalization beyond the three previous cases would
be achieved. However, since only marginal changes are considered, it only needs to be assumed that this
stable relationship holds in the relevant range of indebtedness, around the levels that have been actually
observed during the crisis. Therefore, although still restricted, this provides a meaningful
generalization.
Then dpJ/dDj=s.'dp,/dDj, where so' is the derivative of p0 with respect to p,. Then:
(7) pp-po = c(dpp/dD. - dpp/dDp),
where c =Dp + s.'D. > 0. Equations (5)-(7) can be generalized to an arbitrary number of official creditors,
for example multilateral and bilateral. Let sm..] and sb[.] be the corresponding price-sharing functions.
In that case, two equations (7) would result, referring to the price gap of multilateral and bilateral debt
respectively: pp-Pm = c(dpp/dDm - dpp/dDp) and Pp-Pb = c(dpp/dDb - dpp/dDp), where
c=Dp+sm'Df+Sb'Db. The important thing to notice is that c is the same in both equations. This implies
that the difference in prices is proportional to the difference in the derivatives of the price of private debt
with respect to the corresponding debt stocks. Since the constant of proportionality c is the same for all
classes of creditors, the estimated marginal change in the private price when the face value of debt of
various creditors change can be used to rank their implied prices. Positive correlation of the price
movements, as in the simple seniority cases analyzed, is a sufficient condition for c to be positive.
Assuming more generally that the functions s[.] are arbitrary distribution functions, that is non-decreasing
functions mapping into [0,1], c>0 and price gaps can be signed and ranked by looking at the derivative
differential.
In order to arrive at an empirically estimable specification, assumptions on the sharing
arrangements need to be made. Assume (without loss of generality in the context of ability-to-pay models
as described above) that the value of private debt Vp is:
(8) ppDp = wV[Dp] + (l-w)(V[D9+DP]-V[DJ),
where w is a weight which might depend on the face value of both debts. The value of official debt V.
is obtained by combining (5) and (8): p0D. = (1-w)V[D0] + w(V[D.+Dp]-V[Dp]). Arbitrary sharing rules
can be generated by considering arbitrary weight functions w. Note that the three seniority cases
described above are special cases of this formulation. Private seniority is obtained with w= 1, official
seniority is obtained with w=O, and equal seniority and sharing is obtained for an intermediate value
w=w* vhich makes pp=p0.
The weight w* is in general a function of both face values. Assuming that the increasing and
concave value function V[D] = ADa, 0 < a < 1, it can be checked that w* is a function of the share of
9AI results go through if total debt D is also an argument of the function sol.].
13
relative exposures f=Dp/D0 only. An interesting family of multi-creditor value functions is one where the
total value function V[D] = ADa, 0 < a < 1, and the weight w depends on relative exposure (w[f]), of which
the seniority cases are special cases. Dividing (8) by Dp and manipulating we obtain:
(9) pp = Ah[fl(Dpr ,
where h[fl is a function of relative exposure f (in the case of equal seniority, h[f] =(1 + 1,fH)W). In this
specification, the secondary market price depends not only on the face value of private debt (a decreasing
convex function, as implied by the concavity of the value functio.n) but also on the share of private to
official debt. To the extent that, ceteris paribus, additional official claims diminish the value of private
claims and therefore their price, an increasing function h[f] can be expected.
All of the above can be generalized to the case of several creditors. In particular, if official
creditors are classified into multilateral and bilateral, then equation (9) is generalized by considering
f= DP/DD. fb=DP/Db, and h[fm,fb- (where the function h is expected to be increasing in both arguments).
In section IV, a version of (9) is empirically estimated, where the constant A is modelled in terms of time
and country-specific characteristics and h[.1 is specified in a parametric way which provides a flexible
approximation to arbitrary sharing rules, of which the cases studied under the seniority model are
particular cases.
Generality and limitations of the model
To the extent that the assumption leading.to equation (9), which holds for seniority sharing rules,
is a reasonable approximation for the true sharing rule, the analysis in equation (9) applies. In this
specification, while total value is a function of total face value, the recovery shares depend on relative
exposure in some arbitrary way. By specifying the estimating equation under these assumptions, we are
able to exploit the power of the single pool assumption, in the spirit of an ability-to-pay model, while
retaining the flexibility of arbitrary sharing rules.
A particular difficulty in this problem which this approach solves is that if official creditors are
not attempting to fully withdraw like private creditors, perhaps, but not necessarily, because their claims
are not impaired, there is no strong connection between the financial value of official claims V0[t] and
current financial flows with the countries. If it is assumed that official creditors are attempting to
withdraw as much as they can given their institutional constraints, then the problem would be similar to
the one for private creditors and relatively straightforward: the future recovery could be estimated based
on the actual net transfers that official creditors have been willing and able to capture in the past. This
is in essence what Berthelemy and Vourc'h (1990) do, where not surprisingly they show that the burden
is being shared according to their net transfers-debt outstanding ratio and that, therefore, private creditors
benefit at the expense of official creditors, particularly multilaterals. The premise that official debt is
impaired and that official creditors are exerting maximum pressure to extract net transfers has no basis
and needs to be substantiated, however. The above model attempts to examine this issue without making
such unwarranted assumptions.
It should be kept in mind that official creditors may be willing to lend even if in so doing they
incur financial losses. This model addresses these financial losses without making assumptions about the
motivations behind the official debt strategy. Financial losses may simply indicate that there are
overriding non-financial concerns, rather than junior status. The value of official debt need not have any
influence on the value of private debt as long as official creditors are expected to be willing to lend, for
good or bad financial reasons. This holds true even if official creditors are absolutely preferred, as long
as they are not expected to be willing to exercise their power. A strong negative relation between the
14
values of different creditors' debt has been typically implied in the context of theoretical models assuming
that there is a seniority structure. The need for the assumption that official creditors are expected to
attempt to withdraw to maximize the recovery value of their claims in order to make valid inferences
about their status of preferred creditor seems to have gone unnoticed. Evidence of a weak effect of
official debt on the price of private debt may indicate that official creditors are not expected to withdraw
when they should according to purely financial criteria, rather than that they are not preferred creditors.
Nevertheless, the implications derived for the financial value of official claims remain valid irrespective
of the motivations of their strategy as long as the market correctly anticipates such strategy.
Regarding limitations, this model makes assumptions that are justified in the case of corporate
debt but may be restrictive in the case of sovereign debt. In the corporate case, the total value of the
resources that the debtor has available for creditors (V) is equal to the value of the value of the firm and
all creditors claim against this single collateral. Furthermore, the laws governing corporate bankruptcy
determine that creditors share this single collateral according to a seniority structure: junior creditors
receive payments only after senior creditors are fully paid, and creditors belonging to the same class share
in proportion to exposure. In the sovereign debt case, however, there is no enforceable international law
making the country's assets available to external creditors and determining a seniority structure among
creditors. Why a country would pay and how much it can be extracted, both in total and in connection
to each creditor, is not entirely clear but is certainly in the realm of bargaining theory. Whether the
corporate debt model can be still justified is open to questions.
The model above assumes that creditors share a given present value of resources that the country
can be expected to have available for them, in the sense that total value does not depend on the share
composition of debt among creditors (V=V[D]). This assumption is akin to the single collateral of
corporate debt. Even though in the sovereign debt case there is no sizeable collateral as such, this
assumption may still be applicable. To the extent that sovereign debt service is fundamentally determined
by the country's ability to pay somehow defined, which by definition is not dependent on who the
creditors are, the assumption appears reasonable. If, alternatively, debt service is determined by the threat
of sanctions that creditors have at their disposal, then the composition of debt among creditors may
matter. However, when there is a pool of sanctions which are available to all creditors whose punitive
effect does not depend on which creditor class applies them, which implies that once a creditor class
applies a sanction the other classes cannot do additional harm by applying it, then, formally, the ability-
to-pay model is still applicable. In this case the single collateral assumption is also justified: the level of
resources for total debt service is determined through a bargaining process between creditors and the
debtor country based on the penalties resulting from the application of the set of available sanctions,
which act as an implicit collateral determining the total value of debt claims.
If, by contrast, specific sanctions are available only to a particular class of creditor, or,
alternatively, sanctions available to all of them retain some effectiveness even if they are being exercised
by other classes of creditors, then to some extent the value of debt of each creditor class is determined
by its power to apply additional penalties which need not be shared with other creditors. In the extreme
case where each creditor has available specific sanctions, not available to other creditors, then the value
of debt of each creditor would depend only oa its own face value of debt, rather than total face value.
This would correspond to a corporate case where creditors have specific collaterals. In this extreme case,
debt of official creditors would not have any impact on the price of private debt. While in an ability-to-
pay model that would be an indication that the price of official debt is lower than the price of private debt
(official debt would be junior in a seniority model), in this model of creditor-specific collaterals it would
15
provide no information to make any inference. Evidence of a weak effect of official debt on the price of
private debt may indicate that the true model is one where creditor-specific collaterals are important,
rather than that the implied price of official debt is low (that official debt is not senior, so to speak). The
existence of creditor-specific collaterals would bias downwards the implied prices of official debt derived
from "ability-to-pay" models.
While the single collateral assumption can be justified under a variety of circumstances in the
sovereign debt case, the assumption of a seniority structure among creditors appears more difficult to
justify. Since no enforceable international law applies, even in the context of an ability-to-pay model,
and certainly in a model based on the threat of penalties that each creditor may apply, bargaining among
creditors (perhaps over their shared power to exercise sanctions) would determine the applicable sharing
rules. The assumption of seniority sharing rules would be very convenient for the purpose at hand
because it leads to testable implications relating market price derivatives with respect to stocks of debt
and implicit prices, but there is no reason to believe that actual sharing rules would mimic the outcome
of seniority rules. In the model above, flexible sharing rules, which include seniority rules as particular
cases, are allowed in order to approximate the actual sharing arrangements within a family of admissible
sharing rules. We have been able to relax the assumption of seniority sharing rules while retaining our
ability to make useful inferences by showing that its basic implications still hold if it is simply assumed
that prices are directly functionally related in the relevant range. This more general assumption,
however, is still restrictive and may rule out plausible sharing rules.
An additional issue is whether official creditors cooperate rather than being rivals. To the extent
that in the last analysis the industrialized countries are the important decision agents in both cases, either
directly or through their role as shareholders, the cooperation argument appears plausible. Still, it is not
clear what the outcome of such cooperation would be. Bulow and Rogoff (1991) argue that bilateral
creditors tend to bail out multilateral creditors from bad borrowers. If this were true, the depressing
impact of multilateral debt on the price of private debt could be small because additional money from
bilateral sources would be expected in the future to cover obligations with multilaterals. Therefore weak
effects of multilateral debt would occur even though multilateral credit may not be impaired in any way.
The existence of cooperative linkages between official creditors may lead to the derivation of wrong
inferences from the above model in relation to the financial position of each individual official creditor
class. In the context of models like the one above where total value only depends on total face value, and
in particular, if the ability-to-pay assumption applies to official creditors, this particular interaction does
not seem to add much to the determination of the total value of official claims. While it would affect the
value of each individual official creditor, like IBRD, it can be argued that this is not the most interesting
question. To the extent that industrialized countries view the problem in a comprehensive way, this
problem would amount to an irrelevant accounting convention.
VI. EMPIRICAL EVIDENCE
In this section we seek to determine empirically, how the burden of the debt crisis was shared
among different creditors. Contrary to the popular approach, we do not determine burden sharing by
looking at net transfers provided by each class of creditors. Instead, we analyze how the price of private
debt relates to the face value of official and private debt, and derive a ranking of implicit prices for
different classes of debt. Finally, we discuss the implication of these results for creditor seniority and
burden sharing.
16
We estimate the price of private debt within a valuation model that does not make any assumption
about the seniority structure or sharing rules, as discussed in section III. Equation (10) is a parsimonious
empirical counterpart of equation (9):
(10) log pp = log a - aiog libor + ce,log Dp + ci2log Dp/Dm + %3log Dp/Db + e
As specified in the valuation model, the equation includes face value of private debt and relative
exposure of private creditors to multilateral and bilateral creditors. We also include a time trend and
country dummy variables to capture other country and time specific factors not included in our theoretical
model."0 The last term e is the statistical error.
The model is estimated using annual data on 40 countries for the 1986-1989 time period. Table
2 reports the estimation results. It is interesting to note that only the private debt stock has a significant
effect on the secondary market debt price. As expected, the private debt price significantly decreases
with increases in private debt stocks. The estimated coefficients of multilateral or bilateral debt stock are
of opposite sign: increases in bilateral debt stocks appear to decrease private debt price, whereas increases
in multilateral debt stocks lead to its increase. Neither of them is significantly different from zero,
however. As the F tests reported at the foot of Table 2 indicate, it is appropriate to enter debt stocks of
different creditors separately into the regression. Their impacts are significantly different, especially for
private and multilateral debt stocks. Finally, the discount rate libor develops a significant coefficient that
is not significantly different from unity, as expected.
As explained in section III, the difference between the marginal impact of the face value of debt
of different creditors on the price of private debt reveals the difference between the imputed prices of
those claims. Because of the logarithmic specification of the estimated equation, to get the relevant
derivatives, the log-derivatives reported in Table 2 are elasticities that need to be multiplied by their
corresponding price to debt ratios for each country.
Table 3 reports the calculated derivative differences for each country in the sample. Dervative
differences are reported for 1989 as well as average for the period 1986-89. The difference of the first
two derivatives (dp,/dD,-dp,/dDb) is equal to the difference between bilateral debt price and private debt
price (Pb-p.) times a positive constant c. The difference of the second pair of derivatives (dpM/dDP-
dpp/dDm) is equal to the difference between multilateral and private debt prices times c. Table 3 shows
that there are only wo cases observed in our sample. The most common one, which holds for 26 out
of 40 countries is the case where both differences are negative, with the second one being greater in
absolute value. This implies a price ranking with private price being the highest and multilateral price
the lowest (Pm < Pb < pp). The other case, which holds for 14 out of 40 countries is the one where the first
difference is positive but the second is negative which implies that multilateral price is the lowest but
bilateral price is the highest (p.